论文标题
shimura品种和亚洲的封面
Shimura varieties and abelian covers of the line
论文作者
论文摘要
我们证明，在某些条件下，关于单片的某些条件，投影线的Abelian封面家族不会引起$ a_g $的（较高维度）Shimura subvarieties。这是通过减少到$ p $参数来实现的。我们还使用另一种基于单片计算的方法，以表明上述基因座中的二维亚变化并不特别。特别是表明此类家庭通常具有较大的单型组。与我们先前的结果一起，上述结果有助于对特殊家庭分类在阿贝尔品种的模量空间中，并部分完成了几位作者的工作，包括作者以前的作品。
We prove that under some conditions on the monodromy, families of abelian covers of the projective line do not give rise to (higher dimensional) Shimura subvarieties in $A_g$. This is achieved by a reduction to $p$ argument. We also use another method based on monodromy computations to show that two dimensional subvarieties in the above locus are not special. In particular it is shown that such families have usually large monodromy groups. Together with our earlier results, the above mentioned results contribute to classifying the special families in the moduli space of abelian varieties and partially completes the work of several authors including the author's previous work.
